The present invention generally relates to tuning musical instruments, and more particularly, to methods and apparatus for use in the tuning of musical instruments having a plurality of adjustable frequency tone generators.
Musical instruments having a plurality of adjustable tone generators, or notes, are typically manually tuned by skilled technicians. In the tuning of a particular instrument, the technician, such as a piano tuning technician, relies upon the fundamental frequency as well as other additional frequencies produced by each note. In theory, each additional frequency produced for each note is a xe2x80x9charmonicxe2x80x9d or integer multiple of the base frequency of the note. Furthermore, certain harmonics of a note have theoretical mathematical relationships with harmonics of other notes, allowing the technician to rely upon xe2x80x9cconsonancexe2x80x9d between a note being tuned and a reference note.
However, in actuality, the relationships among the frequencies do not exactly follow the mathematical theory. Deviations from the ideal frequencies are caused by physical characteristics of the tone generators. For instance, in a piano, the thickness and the stiffness of the strings cause these deviations from the mathematical ideals. The actual frequencies produced by a tone generator are conventionally referred to as xe2x80x9cpartials.xe2x80x9d The phenomena causing the deviations between the actual partials and the ideal harmonics of a tone generator is often referred to as the xe2x80x9cinharmonicityxe2x80x9d of the musical instrument. The inharmonicity of a piano causes the partials of a vibrating piano string to be sharper or higher in frequency than would be expected from the harmonics for the string. Furthermore, other effects associated with the particular construction of an instrument can produce a related phenomenon resulting in the partials being be lower or flatter in frequency than the corresponding theoretical harmonic.
If the frequencies of the notes are tuned simply relying on theoretical mathematical relations, inharmonicity causes the piano to sound out of tune. Therefore, inharmonicity forces a technician to xe2x80x9cstretch octavesxe2x80x9d in order for them to sound pleasing.
Manual aural tuning continues to be the preferred method of tuning instruments such as the piano. However, tuning is a complex iterative aural process which requires a high level of skill and practical experience, as well as a substantial amount of time. Some prior methods and devices have sought to simplify the tuning process by providing calculations of estimated tuning, frequencies.
One such method and device is disclosed in U.S. Pat. No. 3,968,719, and later improved upon in U.S. Pat. No. 5,285,711, both issued to Sanderson. In the latter patent, an electrical tuning device measures the inharmonicity between two partials on each of three notes and calculates an eighty-eight (88) note tuning curve. The calculation of the eighty-eight (88) note tuning is performed using equations which rely on inharmonicity constants calculated from only three measured notes.
A problem with the method and device disclosed by the Sanderson patent is that the inharmonicity constants determined from just three notes are either not accurate or are not accurate for the entire instrument being tuned. It is also inflexible in that it does not allow using different octave stretches specific to certain note ranges, as is conventional in aural tuning.
Another method is disclosed in U.S. Pat. Nos. 5,719,343, 5,773,737, 5,814,748, and 5,929,358, all issued to Reyburn. The Reyburn patents describe a method where the tunings of the A notes are calculated with regard to an instrument""s measured inharmonicity of these same A notes, and the remainder of the notes are calculated as an apportionment of the octaves formed by these A notes.
Both the Sanderson and the Reyburn methods are limited in that they can only base calculations on a small number of inharmonicity readings. Since only one partial is being tuned per note, the lack of inharmonicity readings leaves the frequencies of the remaining partials as only estimates. As a consequence, it is difficult to obtain smoothly progressing intervals using the Sanderson or Reyburn methods and devices. Furthermore, these methods require time consuming measurements before actual tuning can begin, in which it is only practical to measure a few notes, therefore leaving the calculations to estimate the inharmonicity of the remaining notes.
Most aural tuning technicians usually visit notes only once and consider several partials of each note being tuned by using aural interval tests. The prior methods are contrary to this preferred method in that some notes must be visited twice, once during measuring and once during tuning. Moreover, none of the prior methods consider multiple partials for all the notes.
The Reyburn patents also disclose a method for digitally measuring wavelengths and frequencies by counting the number of samples between the zero crossing points at the starting and ending times of a sequence of cycles of a signal over a period of time approaching 300 milliseconds. These methods are limited in their accuracy because they depend on the sample rate and do not evaluate the regularity of the measurements to determine during which time periods the frequency has settled into a consistent state.
The Reyburn patents also disclose a device and a method for automatically detecting which note has been energized by the technician. The device filters a signal for a particular partial that would be produced by a note within one to four notes of the one previously energized. The drawback to this method is that there is a limited range of movement to which the technician is confined, notes of different octaves are indistinguishable, and it is not possible to jump to any note on the instrument.
Prior tuning displays use the metaphor of movement or rotation to indicate whether the note being tuned is sharp or flat as compared to a reference frequency, and the speed of movement or rotation indicates by how much. U.S. Pat. No. 3,982,184, issued to Sanderson, describes a display like this based on the phase difference of two signals; however it is severely limited in its sensitivity to display phase differences less than 90xc2x0. The Reyburn patents describe a rotating display that is based on pitch and not phase. This has the limitation of a slow response since it must measure the pitch over a series of many cycles before a change in the display can be effected.
An ideal electronic tuning device would provide the technician with the best quality tuning possible with the least number of actions. Furthermore, since inharmonicity is not entirely consistent from one note to the next, an ideal electronic tuning device would assist the technician in making compromises so that the majority of intervals sound correct, with each of the intervals being determined by different partials. The ideal electronic tuning device would calculate wavelengths and frequencies in a precise manner with some consideration of the quality of the signal and calculation. The ideal electronic tuning device would also allow for automatic note detection of any note on an instrument at any time.
Accordingly, there continues to be a need for an improved tuning method and device which can assist technicians in providing more accurate and efficient tuning of musical instruments.
Therefore, the present invention provides novel tuning methods and systems which allow for accurate tuning of musical instruments having inharmonicity by considering multiple partials of each and every note.
In one aspect of the invention, a method is provided for use in the tuning of a musical instrument having multiple adjustable frequency tone generators. The method includes measuring two or more partials for each of one or more of the multiple tone generators. From the measured partials, one or more inharmonicity values are calculated, each inharmonicity value representing a relationship between two of the partials of a respective tone generator. Then one or more inharmonicity values are estimated for one or more of the unmeasured tone generators of the multiple tone generators. A target frequency is then calculated for one or more partials of one or more tone generators based upon the calculated inharmonicity value(s) and the estimated inharmonicity value(s).
In another aspect of the invention, another method is provided for use in the tuning of a musical instrument having multiple adjustable frequency tone generators. The method includes measuring three or more partials of a first tone generator, and calculating three or more inharmonicity values, each inharmonicity value representing a relationship between two of the measured partials of the first tone generator. Then one or more inharmonicity values are estimated for each of a plurality of the multiple tone generators, each estimated inharmonicity value representing a relationship between two estimated partials of the respective tone generator. A target frequency is then calculated for one or more partials of the first tone generator based upon one or more of the calculated inharmonicity values and one or more of the estimated inharmonicity values.
In yet another aspect of the invention, a system for use in the tuning of musical instrument having multiple adjustable frequency tone generators includes a wave sampler, a signal processor, and a tuning calculator. The wave sampler is capable of converting sound into an electrical signal. The signal processor receives the signal, and is adapted to measure a plurality of partials based upon the signal. The signal processor is adapted to generate a plurality of inharmonicity values, each inharmonicity value representing a relationship between two of said measured plurality of partials of a respective tone generator. The tuning calculator is capable of calculating a target frequency for one or more partials of one or more tone generators based upon the inharmonicity values.
In another aspect of the invention, another method is provided for use in single pass tuning of a musical instrument having multiple adjustable frequency tone generators. The method includes the measurement of two or more partials of a first tone generator, and the calculation of a target frequency for each of one or more partials of each of a plurality of tone generators. A target frequency is then generated for the first tone generator, and the first tone generator is adjusted based upon the generated target frequency. Next, one or more partials of another tone generator are measured, and a target frequency is calculated for each of one or more partials of each of a plurality of tone generators. The tone generator is adjusted in response to the generated target frequency. The measurement, calculation, and adjustment for other tone generators is repeated until substantially all of the plurality of tone generators have been adjusted. Each of the plurality of the multiple tone generators is adjusted to a final state before another tone generator is measured, and no other tone generators are measured before the first tone generator is adjusted.